Analyzing the horizontal orientation of the crustal stress adjacent to plate boundaries

The spatial analysis of horizontal stress orientation is important to study stress sources and understand tectonics and the deformation of the lithosphere. Additional to the stress sources, the geometry of stress fields depends on the underlying coordinate reference system, which causes spatial distortions that bias the analysis and interpretation of stresses. The bias can be avoided when the stress field is decomposed and transformed into the reference frame of its first-order stress source. We present a modified and extended theory based on the empirical link between the orientation of first-order stresses and the trajectories of lateral plate boundary forces. This link is applied to analyze the orientation of horizontal stresses, their patterns, and tectonic structures from the perspective of their first-order source or cause. By using only parameters for the relative motion between two neighboring plates, we model the first-order orientation of the maximum horizontal stress that statistically fits the orientation of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ge$$\end{document}≥80% of the global stress data adjacent to plate boundaries. Considerable deviations of the observed stress from the predicted first-order stress direction can reveal the geometry of second-order stresses and confine areas where other stress sources dominate. The model’s simple assumptions, independence from the sample size, potential application to regional to global scale analysis, and compatibility with other spatial interpolation algorithms make it a powerful method for analyzing stress fields. For immediate use, the presented method is implemented in the free and open-source software package tectonicr, which is written in the computer language R.

Analyzing the horizontal orientation of the crustal stress adjacent to plate boundaries: Supplementary Information Tobias Stephan, Eva Enkelmann, Uwe Kroner April 27, 2023

Conversion between geographical and Cartesian coordinates
The coordinate conversion of a vector given in geographical coordinates (latitude λ and longitude φ ) into Cartesian coordinates is The conversion into geographical coordinates is 2 Implementation in R The presented method and the example dataset are implemented in the free and open-source software package tectonicr that is written in the computer language R. As a R-based cross-platform program, tectonicr works on Windows © , MacOS X © and GNU/Linux.The source code for the program is made available under the GNU GPL license v3.0, which permits re-use and modification provided that any derived code is released under the same conditions (Free Software Foundation, 2007).The entire source code of tectonicr is accessible through the Comprehensive R Archive Network (CRAN)1 and can be accessed through R's command line: install .packages ( " tectonicr " ) library ( " tectonicr " ) The latest version can be obtained from the GitHub repository (https://github.com/tobiste/tectonicr)requiring the package remotes: install .packages ( " remotes " ) remotes :: install _ github ( " tobiste / tectonicr " ) library ( " tectonicr " ) The following code reproduces the examples used in the study.It transforms the San Andreas Fault-Gulf of California stress dataset into the coordinate reference system of the North America-Pacific plate motion, evaluates the transformed stress orientations in terms of a right-lateral plate boundary displacement, and visualizes the results: # Load the San Andreas -Gulf of California dataset : data ( " san _ andreas " ) # Load plate boundary geometries data ( " plates " ) # Extract boundary between Pacific ( pa ) and North American ( na ) plates na _ pa _ boundary <-subset ( plates , plates $ pair == " na -pa " ) # Load the current plate motion ( cpm ) models : data ( " cpm _ models " ) morvel <-subset ( cpm _ models , cpm _ models $ model == " NNR -MORVEL 5 6 " ) # select MORVEL model # Relative plate motion between Pacific and North American plates : na _ pa <-equivalent _ rotation ( morvel , fixed = " na " , rot = " pa " ) # Transform stress data set and test against predicted left -lateral tangential plate boundary ( left ) : stress _ analysis ( san _ andreas , euler = na _ pa , type = " right " , pb = na _ pa _ boundary ) # Interpolate the stress field in the PoR coordinate system : PoR _ stress 2 grid ( san _ andreas , na _ pa ) The stress data used for the Himalaya-Tibet and North Atlantic Ridge-Iceland areas can be obtained and processed through the following code: data ( " tibet " ) eu _ in _ boundary <-subset ( plates , plates $ pair == " eu -in " ) eu _ in <-equivalent _ rotation ( morvel , fixed = " eu " , rot = " in " ) stress _ analysis ( tibet , euler = eu _ in , type = " in " , pb = eu _ in _ boundary ) PoR _ stress 2 grid ( tibet , eu _ in ) data ( " iceland " ) eu _ na _ boundary <-subset ( plates , plates $ pair == " eu -na " ) eu _ na <-equivalent _ rotation ( morvel , fixed = " na " , rot = " eu " ) stress _ analysis ( iceland , euler = eu _ na , type = " out " , pb = eu _ na _ boundary ) PoR _ stress 2 grid ( iceland , eu _ na ) 3 Test results and spatial interpolation san_andreas.csvDataset of the San Andreas Fault-Gulf of California region (snippet from the WSM2016 database, table column headers are identical to the database).
san_andreas_smooth.csvSmoothed stress field for the San Andreas Fault-Gulf of California region as comma-separated text file (as shown in Supplementary Figure S1A).
san_andreas_smooth_shp.zip Smoothed stress field for the San Andreas Fault-Gulf of California region as ESRI shapefile.
asia.csv Dataset of Central Asia (snippet from the WSM2016 database) tibet_smooth.csvSmoothed stress field for the Himalaya-Tibet region as comma-separated text file (as shown in Supplementary Figure S1B).
tibet_smooth_shp.zipSmoothed stress field for the Himalaya-Tibet region as ESRI shapefile.
iceland.csv Dataset of the North Atlantic Ridge-Iceland region (snippet from the WSM2016 database) iceland_smooth.csvSmoothed stress field for the North Atlantic Ridge-Iceland region as comma-separated text file (as shown in Supplementary Figure S1C).
iceland_smooth_shp.zipSmoothed stress field for the North Atlantic Ridge-Iceland region as ESRI shapefile.
Datasets used in this study are extracted from the WSM2016 database.Hence, table columns of the files are named as in the database.The generated datasets contain the additional columns:

Table S1 .
plate_boundaries.zipGeometries of the plate boundaries (from Bird 2003) with characterization of the plate boundary displacement type (ESRI shapefile).global_gsrm.csvTestresults for the global plate boundaries using GSRM v2.1 global_morvel.csvTestresults for the global plate boundaries using MORVEL56 global_nuvel.csvTestresults for the global plate boundaries using NUVEL-1A global_revel.csvTestresults for the global plate boundaries using REVELDatasets used for the interpolation are extracted from the WSM2016 database.Hence, table columns of the files are named as in the database.The generated datasets contain the additional columns as described in Section 3 Statistical summary of testing global plate boundary zones (≤1500 km from plate boundary) using different models for current plate motion.Transform plate boundaries are either right-lateral (R) or left-lateral (L).The observed azimuth is the weighted circular median and the circular quasi-interquartile range of the PoR-transformed σ Hmax azimuths.